(CNN) -- A mother in Tampa, Florida has admitted in detail to killing her two teen-aged children, police said.

Police checking on the family at the request of a relative found Julie K. Schenecker, 50, on the back porch of her home Friday morning, dressed in blood-covered clothing, according to a police statement.

They found her son, Beau Powers Schenecker, 13, dead in the family's SUV, which had been parked in the garage, the statement said. Calyx Powers Schenecker, 16, was in an upstairs bedroom, also dead.

"She did tell us that they talked back, that they were mouthy," Tampa police spokeswoman Laura McElroy told CNN affiliate WTSP. "But I don't think that will ever serve as an explanation to the rest of us of how you could take a child's life."

The woman shot her son as she drove him to soccer practice and returned home to shoot her daughter as she studied on her computer, CNN affiliate WFTS reported, citing investigators.

The preliminary investigation indicates that the teens were killed on Thursday evening, a police statement said, but a medical county examiner will determine the time of death.

Police have charged the mother in the killings, the police statement said.

Police were called to the house after Schenecker's mother called from Texas to express concern about her daughter's welfare, saying she was depressed, the police statement said.

Schenecker was initially booked into jail, but was transferred to Tampa General Hospital for treatment of an existing medical condition, according to the Hillsborough County Sheriff's Office, WTSP reported.

Hundreds of people attended a candlelight vigil on Friday night in memory of the siblings, according to WTSP.

"It's just sad that his mom did this to him and his sister because he didn't deserve this," one of the mourners, Hailey Johnson, told WTSP. "He was the sweetest kid ever."

"I came out here tonight because I just needed to show respect and show that I really did care about Beau," said another mourner, teenager Ann Sloan.